Question

ABC IS A TRIANGLE RIGHT ANGLED AT B SUCH THAT ANGLE BCA=2ANGLE BAC . SHOW THAT AC=2BC

Answer 1

$\huge\sf\blue{Given}$

✭ ∠BCA = 2∠BAC

✭ ∆ABC is a right angle triangle right angled at B

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$\huge\sf\gray{To \: Prove}$

◈ AC = 2BC

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$\huge\sf\purple{Steps}$

$\large\underline{\underline{\sf Let}}$

◕ ∠BCA = x

◕ ∠BAC = 2x

We know that in a triangle the angles add up to 180°, so

➝ $\sf \angle BAC + \angle BCA + \angle + \angle ABC = 180^{\circ}$

➝ $\sf 2x + x +90^{\circ} = 180^{\circ}$

➝ $\sf 3x = 180-90$

➝ $\sf 3x = 90$

➝ $\sf x = \dfrac{90}{3}$

➝ $\sf \green{x = 30}$

$\sf \bullet \angle BCA = x = 30^{\circ}$

$\sf \bullet \angle BAC = 2x = 2(30) = 60^{\circ}$

$\sf Hence \ Proved!!$

$\sf \sf\star\: Diagram \:\star$

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